The authors model a pay relationship and find support for their model. Without getting into the gory details of the modeling, consider two firms (one large, one small) and two managers (one talented, one less so) whose abilities are unknown but can be learned via observation. How much the firms would pay (their reservation price) and how much the managers would accept (their reservation price) are examined.

"...panel data for 1992-2006 exclusive of time factors, which strikingly suggest that the average talent level of small firm CEOs is only slightly lower than that of large firm CEOs, but the talent variability of small firm CEOs is far greater than that of large firms."

A few look-ins.

"...each firm would like to hire an agent who would produce an expected profit to the firm at least as great as the other agent would. However, each firm’s decision can also affect/be affected by the other firm’s decision."

and in examining the pay and performance relation the authors report:

"CEOs employed by firms with positive performance capture over 67% theirexceptional talent in the form of higher pay. By contrast, for negative performers therelationship is insignificant indicating the absence of penalty for poor performance.This would indicate that incentive contracts treat negative performance as having acomponent of bad luck with less severe penalties in place which is more conducive torisk-taking."

They also report (and I find myself thinking of professional sports teams here) that large firms can afford to hire some lower level talent and essentially overpay.

"...when a large firm hires a low-ability manager, the expected pay for the low ability manager can be higher than that for a high-ability manager who is hired by a small firm, if the large firm’s productivity and the firm size are sufficiently higher and larger than those of the small firm"

Moreover the authors examine the informational effect of having worked at one firm and then switching. (Intuitively, consider that a manager with low skills will be 'found out' by larger firms. Thus switching firms at least potentially signals lower abilities). To protect themselves, the smaller firms would want to make a more incentive laden contract. To wit:

"..that a manager who previously worked for a large firm will be given a contract with a higher sensitivity than a manager who previously worked for a small firm. We find significant statistical support for this hypothesis."

Interesting stuff. If I were a general manager of a professional sports team, I would definitely want to read this one.